91av

#206 All square

Set by Colin Beveridge

“What ho!” boomed Aunt Nicola. I could tell she was about to talk cricket at me. “Have you been following the test match between Pythagorea and Lagrangia?”

“Auntie, you know I prefer Navier-Stokes to Ben Stokes.” “Well,” she said, “you might be interested – there’s maths involved! In their first innings, Lagrangia’s total score was a square number.”

“Innings?” I asked. “It’s the word for a team’s turn to bat. They each have two. In their first, the Pythagoreans also got a square number, but they were more than 300 behind!”

“That sounds insurmountable.” “You might think so,” she said. “Then, when Lagrangia batted again, they added a different square number – less than 50 – so that their lead and overall total were also square numbers.”

“Goodness.” “But the Pythagoreans battled back in their second innings,” she continued, “and the game ended dramatically in a tie.”

I then knew enough to work out the totals of the four innings in order. What were they?

Solution next week

#205 Buried shields

Solution

The missing section of the broken shield can’t be silver or gold, as those colours would create a shield that is already pictured, so it must be blue.

There are already three shields with two blue sections, as well as three with two grey sections, so the ninth shield must have two gold sections.

The only combination that isn’t already pictured is shown above.